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Nan Chen

Publications and source records attributed to Nan Chen.

At least 91 records · Page 5Linked to original sources
arXiv2023

Snapp: An Agile Robotic Fish with 3-D Maneuverability for Open Water Swim

Fish exhibit impressive locomotive performance and agility in complex underwater environments, using their undulating tails and pectoral fins for propulsion and maneuverability. Replicating these abilities in robotic fish is challenging; existing designs focus on either fast swimming or directional control at limited speeds, mainly within a confined environment. To address these limitations, we designed Snapp, an integrated robotic fish capable of swimming in open water with high speeds and full 3-dimensional maneuverability. A novel cyclic-differential method is layered on the mechanism. It integrates propulsion and yaw-steering for fast course corrections. Two independent pectoral fins provide pitch and roll control. We evaluated Snapp in open water environments. We demonstrated significant improvements in speed and maneuverability, achieving swimming speeds of 1.5 m/s (1.7 Body Lengths per second) and performing complex maneuvers, such as a figure-8 and S-shape trajectory. Instantaneous yaw changes of 15$^{\circ}$ in 0.4 s, a minimum turn radius of 0.85 m, and maximum pitch and roll rates of 3.5 rad/s and 1 rad/s, respectively, were recorded. Our results suggest that Snapp's swimming capabilities have excellent practical prospects for open seas and contribute significantly to developing agile robotic fishes.

cs.RO↗
arXiv2023

Particle-Continuum Multiscale Modeling of Sea Ice Floes

Sea ice profoundly influences the polar environment and the global climate. Traditionally, Sea ice has been modeled as a continuum under Eulerian coordinates to describe its large-scale features, using, for instance, viscous-plastic rheology. Recently, Lagrangian particle models, also known as the discrete element method (DEM) models, have been utilized for characterizing the motion of individual sea ice fragments (called floes) at scales of 10 km and smaller, especially in marginal ice zones. This paper develops a multiscale model that couples the particle and the continuum systems to facilitate an effective representation of the dynamical and statistical features of sea ice across different scales. The multiscale model exploits a Boltzmann-type system that links the particle movement with the continuum equations. For the small-scale dynamics, it describes the motion of each sea ice floe. Then, as the large-scale continuum component, it treats the statistical moments of mass density and linear and angular velocities. The evolution of these statistics affects the motion of individual floes, which in turn provides bulk feedback that adjusts the large-scale dynamics. Notably, the particle model characterizing the sea ice floes is localized and fully parallelized, in a framework that is sometimes called superparameterization, which significantly improves computation efficiency. Numerical examples demonstrate the effective performance of the multiscale model. Additionally, the study demonstrates that the multiscale model has a linear-order approximation to the truth model.

math.NA↗
arXiv2023

Calliope-Net: Automatic Generation of Graph Data Facts via Annotated Node-link Diagrams

Graph or network data are widely studied in both data mining and visualization communities to review the relationship among different entities and groups. The data facts derived from graph visual analysis are important to help understand the social structures of complex data, especially for data journalism. However, it is challenging for data journalists to discover graph data facts and manually organize correlated facts around a meaningful topic due to the complexity of graph data and the difficulty to interpret graph narratives. Therefore, we present an automatic graph facts generation system, Calliope-Net, which consists of a fact discovery module, a fact organization module, and a visualization module. It creates annotated node-link diagrams with facts automatically discovered and organized from network data. A novel layout algorithm is designed to present meaningful and visually appealing annotated graphs. We evaluate the proposed system with two case studies and an in-lab user study. The results show that Calliope-Net can benefit users in discovering and understanding graph data facts with visually pleasing annotated visualizations.

cs.HC↗
arXiv2023

Effective Statistical Control Strategies for Complex Turbulent Dynamical Systems

Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling the statistical features of a turbulent system offers a more robust and efficient approach. Crude first-order linear response approximations were typically employed in previous works for statistical control with small initial perturbations. This paper aims to develop two new statistical control strategies for scenarios with more significant initial perturbations and stronger nonlinear responses, allowing the statistical control framework to be applied to a much wider range of problems. First, higher-order methods, incorporating the second-order terms, are developed to resolve the full control-forcing relation. The corresponding changes to recovering the forcing perturbation effectively improve the performance of the statistical control strategy. Second, a mean closure model for the mean response is developed, which is based on the explicit mean dynamics given by the underlying turbulent dynamical system. The dependence of the mean dynamics on higher-order moments is closed using linear response theory but for the response of the second-order moments to the forcing perturbation rather than the mean response directly. The performance of these methods is evaluated extensively on prototype nonlinear test models, which exhibit crucial turbulent features, including non-Gaussian statistics and regime switching with large initial perturbations. The numerical results illustrate the feasibility of different approaches due to their physical and statistical structures and provide detailed guidelines for choosing the most suitable method based on the model properties.

math.DS↗
arXiv2023

Trajectory Generation and Tracking Control for Aggressive Tail-Sitter Flights

We address the theoretical and practical problems related to the trajectory generation and tracking control of tail-sitter UAVs. Theoretically, we focus on the differential flatness property with full exploitation of actual UAV aerodynamic models, which lays a foundation for generating dynamically feasible trajectory and achieving high-performance tracking control. We have found that a tail-sitter is differentially flat with accurate aerodynamic models within the entire flight envelope, by specifying coordinate flight condition and choosing the vehicle position as the flat output. This fundamental property allows us to fully exploit the high-fidelity aerodynamic models in the trajectory planning and tracking control to achieve accurate tail-sitter flights. Particularly, an optimization-based trajectory planner for tail-sitters is proposed to design high-quality, smooth trajectories with consideration of kinodynamic constraints, singularity-free constraints and actuator saturation. The planned trajectory of flat output is transformed to state trajectory in real-time with consideration of wind in environments. To track the state trajectory, a global, singularity-free, and minimally-parameterized on-manifold MPC is developed, which fully leverages the accurate aerodynamic model to achieve high-accuracy trajectory tracking within the whole flight envelope. The effectiveness of the proposed framework is demonstrated through extensive real-world experiments in both indoor and outdoor field tests, including agile SE(3) flight through consecutive narrow windows requiring specific attitude and with speed up to 10m/s, typical tail-sitter maneuvers (transition, level flight and loiter) with speed up to 20m/s, and extremely aggressive aerobatic maneuvers (Wingover, Loop, Vertical Eight and Cuban Eight) with acceleration up to 2.5g.

cs.RO↗
arXiv2023

Launching Drifter Observations in the Presence of Uncertainty

Determining the optimal locations for placing extra observational measurements has practical significance. However, the exact underlying flow field is never known in practice. Significant uncertainty appears when the flow field is inferred from a limited number of existing observations via data assimilation or statistical forecast. In this paper, a new computationally efficient strategy for deploying Lagrangian drifters that highlights the central role of uncertainty is developed. A nonlinear trajectory diagnostic approach that underlines the importance of uncertainty is built to construct a phase portrait map. It consists of both the geometric structure of the underlying flow field and the uncertainty in the estimated state from Lagrangian data assimilation. The drifters are deployed at the maxima of this map and are required to be separated enough. Such a strategy allows the drifters to travel the longest distances to collect both the local and global information of the flow field. It also facilitates the reduction of a significant amount of uncertainty. To characterize the uncertainty, the estimated state is given by a probability density function (PDF). An information metric is then introduced to assess the information gain in such a PDF, which is fundamentally different from the traditional path-wise measurements. The information metric also avoids using the unknown truth to quantify the uncertainty reduction, making the method practical. Mathematical analysis exploiting simple illustrative examples is used to validate the strategy. Numerical simulations based on multiscale turbulent flows are then adopted to demonstrate the advantages of this strategy over some other methods.

physics.flu-dyn↗
arXiv2023

Lagrangian Descriptors with Uncertainty

Lagrangian descriptors provide a global dynamical picture of the geometric structures for arbitrarily time-dependent flows with broad applications. This paper develops a mathematical framework for computing Lagrangian descriptors when uncertainty appears. The uncertainty originates from estimating the underlying flow field as a natural consequence of data assimilation or statistical forecast. It also appears in the resulting Lagrangian trajectories. The uncertainty in the flow field directly affects the path integration of the crucial nonlinear positive scalar function in computing the Lagrangian descriptor, making it fundamentally different from many other diagnostic methods. Despite being highly nonlinear and non-Gaussian, closed analytic formulae are developed to efficiently compute the expectation of such a scalar function due to the uncertain velocity field by exploiting suitable approximations. A rapid and accurate sampling algorithm is then built to assist the forecast of the probability density function (PDF) of the Lagrangian trajectories. Such a PDF provides the weight to combine the Lagrangian descriptors along different paths. Simple but illustrative examples are designed to show the distinguished behavior of using Lagrangian descriptors in revealing the flow field when uncertainty appears. Uncertainty can either completely erode the coherent structure or barely affect the underlying geometry of the flow field. The method is also applied for eddy identification, indicating that uncertainty has distinct impacts on detecting eddies at different time scales. Finally, when uncertainty is incorporated into the Lagrangian descriptor for inferring the source target, the likelihood criterion provides a very different conclusion from the deterministic methods.

physics.flu-dyn↗
arXiv2023

Uncertainty Quantification of Nonlinear Lagrangian Data Assimilation Using Linear Stochastic Forecast Models

Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact Bayesian formulae for the state estimation of high-dimensional systems. In this paper, an analytically tractable mathematical framework for continuous-in-time Lagrangian data assimilation is developed. It preserves the nonlinearity in the observational processes while approximating the forecast model of the underlying flow field using linear stochastic models (LSMs). A critical feature of the framework is that closed analytic formulae are available for solving the posterior distribution, which facilitates mathematical analysis and numerical simulations. First, an efficient iterative algorithm is developed in light of the analytically tractable statistics. It accurately estimates the parameters in the LSMs using only a small number of the observed tracer trajectories. Next, the framework facilitates the development of several computationally efficient approximate filters and the quantification of the associated uncertainties. A cheap approximate filter with a diagonal posterior covariance derived from the asymptotic analysis of the posterior estimate is shown to be skillful in recovering incompressible flows. It is also demonstrated that randomly selecting a small number of tracers at each time step as observations can reduce the computational cost while retaining the data assimilation accuracy. Finally, based on a prototype model in geophysics, the framework with LSMs is shown to be skillful in filtering nonlinear turbulent flow fields with strong non-Gaussian features.

math.DS↗
arXiv2023

CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting

Regime switching is ubiquitous in many complex dynamical systems with multiscale features, chaotic behavior, and extreme events. In this paper, a causation entropy boosting (CEBoosting) strategy is developed to facilitate the detection of regime switching and the discovery of the dynamics associated with the new regime via online model identification. The causation entropy, which can be efficiently calculated, provides a logic value of each candidate function in a pre-determined library. The reversal of one or a few such causation entropy indicators associated with the model calibrated for the current regime implies the detection of regime switching. Despite the short length of each batch formed by the sequential data, the accumulated value of causation entropy corresponding to a sequence of data batches leads to a robust indicator. With the detected rectification of the model structure, the subsequent parameter estimation becomes a quadratic optimization problem, which is solved using closed analytic formulae. Using the Lorenz 96 model, it is shown that the causation entropy indicator can be efficiently calculated, and the method applies to moderately large dimensional systems. The CEBoosting algorithm is also adaptive to the situation with partial observations. It is shown via a stochastic parameterized model that the CEBoosting strategy can be combined with data assimilation to identify regime switching triggered by the unobserved latent processes. In addition, the CEBoosting method is applied to a nonlinear paradigm model for topographic mean flow interaction, demonstrating the online detection of regime switching in the presence of strong intermittency and extreme events.

math.DS↗
arXiv2023

Data-Driven Statistical Reduced-Order Modeling and Quantification of Polycrystal Mechanics Leading to Porosity-Based Ductile Damage

Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial PDF of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts using physical models often fail to capture the statistics of structural evolution during material deformation. This study proposes a data-driven statistical reduced-order modeling framework to provide a probabilistic forecast of the deformation process leading to porosity-based ductile damage, with uncertainty quantification. The framework starts with computing the time evolution of the leading moments of specific state variables from full-field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is used to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations show that the model can characterize the time evolution of the non-Gaussian PDF of the von Mises stress and quantify the probability of extreme events. The learning process also reveals that the mean stress interacts with higher-order moments and extreme events in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement shows that the leading four moments are sufficient to characterize the crucial non-Gaussian features throughout the entire deformation history.

cond-mat.mtrl-sci↗
arXiv2023

Swarm-LIO: Decentralized Swarm LiDAR-inertial Odometry

Accurate self and relative state estimation are the critical preconditions for completing swarm tasks, e.g., collaborative autonomous exploration, target tracking, search and rescue. This paper proposes Swarm-LIO: a fully decentralized state estimation method for aerial swarm systems, in which each drone performs precise ego-state estimation, exchanges ego-state and mutual observation information by wireless communication, and estimates relative state with respect to (w.r.t.) the rest of UAVs, all in real-time and only based on LiDAR-inertial measurements. A novel 3D LiDAR-based drone detection, identification and tracking method is proposed to obtain observations of teammate drones. The mutual observation measurements are then tightly-coupled with IMU and LiDAR measurements to perform real-time and accurate estimation of ego-state and relative state jointly. Extensive real-world experiments show the broad adaptability to complicated scenarios, including GPS-denied scenes, degenerate scenes for camera (dark night) or LiDAR (facing a single wall). Compared with ground-truth provided by motion capture system, the result shows the centimeter-level localization accuracy which outperforms other state-of-the-art LiDAR-inertial odometry for single UAV system.

cs.RO↗
arXiv2022

Rigorous Derivation of Stochastic Conceptual Models for the El Niño-Southern Oscillation from a Spatially-Extended Dynamical System

El Niño-Southern Oscillation (ENSO) is the most predominant interannual variability in the tropics, significantly impacting global weather and climate. In this paper, a framework of low-order conceptual models for the ENSO is systematically derived from a spatially-extended stochastic dynamical system with full mathematical rigor. The spatially-extended stochastic dynamical system has a linear, deterministic, and stable dynamical core. It also exploits a simple stochastic process with multiplicative noise to parameterize the intraseasonal wind burst activities. A principal component analysis based on the eigenvalue decomposition method is applied to provide a low-order conceptual model that succeeds in characterizing the large-scale dynamical and non-Gaussian statistical features of the eastern Pacific El Niño events. Despite the low dimensionality, the conceptual modeling framework contains outputs for all the atmosphere, ocean, and sea surface temperature components with detailed spatiotemporal patterns. This contrasts with many existing conceptual models focusing only on a small set of specified state variables. The stochastic versions of many state-of-the-art low-order models, such as the recharge-discharge and the delayed oscillators, become special cases within this framework. The rigorous derivation of such low-order models provides a unique way to connect models with different spatiotemporal complexities. The framework also facilitates understanding the instantaneous and memory effects of stochastic noise in contributing to the large-scale dynamics of the ENSO.

physics.geo-ph↗
arXiv2022

Combining Stochastic Parameterized Reduced-Order Models with Machine Learning for Data Assimilation and Uncertainty Quantification with Partial Observations

A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning model that builds a nonlinear map between the coefficients of observed and unobserved state variables for each spectral mode. A cheap low-order nonlinear stochastic parameterized extended Kalman filter (SPEKF) model is employed as the forecast model in the ensemble Kalman filter to deal with each mode associated with the observed variables. The resulting ensemble members are then fed into the machine learning model to create an ensemble of the corresponding unobserved variables. In addition to the ensemble spread, the training residual in the machine learning-induced nonlinear map is further incorporated into the state estimation that advances the quantification of the posterior uncertainty. The hybrid data assimilation algorithm is applied to a precipitating quasi-geostrophic (PQG) model, which includes the effects of water vapor, clouds, and rainfall beyond the classical two-level QG model. The complicated nonlinearities in the PQG equations prevent traditional methods from building simple and accurate reduced-order forecast models. In contrast, the SPEKF model is skillful in recovering the intermittent observed states, and the machine learning model effectively estimates the chaotic unobserved signals. Utilizing the calibrated SPEKF and machine learning models under a moderate cloud fraction, the resulting hybrid data assimilation remains reasonably accurate when applied to other geophysical scenarios with nearly clear skies or relatively heavy rainfall, implying the robustness of the algorithm for extrapolation.

physics.comp-ph↗
arXiv2022

MARSIM: A light-weight point-realistic simulator for LiDAR-based UAVs

The emergence of low-cost, small form factor and light-weight solid-state LiDAR sensors have brought new opportunities for autonomous unmanned aerial vehicles (UAVs) by advancing navigation safety and computation efficiency. Yet the successful developments of LiDAR-based UAVs must rely on extensive simulations. Existing simulators can hardly perform simulations of real-world environments due to the requirements of dense mesh maps that are difficult to obtain. In this paper, we develop a point-realistic simulator of real-world scenes for LiDAR-based UAVs. The key idea is the underlying point rendering method, where we construct a depth image directly from the point cloud map and interpolate it to obtain realistic LiDAR point measurements. Our developed simulator is able to run on a light-weight computing platform and supports the simulation of LiDARs with different resolution and scanning patterns, dynamic obstacles, and multi-UAV systems. Developed in the ROS framework, the simulator can easily communicate with other key modules of an autonomous robot, such as perception, state estimation, planning, and control. Finally, the simulator provides 10 high-resolution point cloud maps of various real-world environments, including forests of different densities, historic building, office, parking garage, and various complex indoor environments. These realistic maps provide diverse testing scenarios for an autonomous UAV. Evaluation results show that the developed simulator achieves superior performance in terms of time and memory consumption against Gazebo and that the simulated UAV flights highly match the actual one in real-world environments. We believe such a point-realistic and light-weight simulator is crucial to bridge the gap between UAV simulation and experiments and will significantly facilitate the research of LiDAR-based autonomous UAVs in the future.

cs.RO↗
arXiv2022

A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about incorrect physics in the presence of random noise and cannot easily handle the situation with incomplete data. In this paper, a new iterative learning algorithm for complex turbulent systems with partial observations is developed that alternates between identifying model structures, recovering unobserved variables, and estimating parameters. First, a causality-based learning approach is utilized for the sparse identification of model structures, which takes into account certain physics knowledge that is pre-learned from data. It has unique advantages in coping with indirect coupling between features and is robust to the stochastic noise. A practical algorithm is designed to facilitate the causal inference for high-dimensional systems. Next, a systematic nonlinear stochastic parameterization is built to characterize the time evolution of the unobserved variables. Closed analytic formula via an efficient nonlinear data assimilation is exploited to sample the trajectories of the unobserved variables, which are then treated as synthetic observations to advance a rapid parameter estimation. Furthermore, the localization of the state variable dependence and the physics constraints are incorporated into the learning procedure, which mitigate the curse of dimensionality and prevent the finite time blow-up issue. Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable stochastic parameterizations for many complex nonlinear systems with chaotic dynamics, spatiotemporal multiscale structures, intermittency, and extreme events.

math.DS↗
arXiv2022

Quantifying the Predictability of ENSO Complexity Using a Statistically Accurate Multiscale Stochastic Model and Information Theory

An information-theoretic framework is developed to assess the predictability of ENSO complexity, which is a central problem in contemporary meteorology with large societal impacts. The information theory advances a unique way to quantify the forecast uncertainty and allows to distinguish the predictability limit of different ENSO events. One key step in applying the framework to compute the information gain representing the predictability is to build a statistically accurate dynamical model. To this end, a recently developed multiscale stochastic model, which succeeds in capturing both the large-scale dynamics and many crucial statistical properties of the observed ENSO complexity, is incorporated into the information-theoretic framework. It is shown that different ENSO events possess very distinct predictability limits. In addition to the ensemble mean, the ensemble spread also has remarkable contributions to the predictability. While the information theory indicates that predicting the onset of the eastern Pacific El Niños is challenging, it reveals a universal tendency to convert strong predictability to skillful forecast for predicting many central Pacific El Niños about two years in advance. In addition, strong predictability is found for the La Niña events, corresponding to the effective discharge process. In the climate change scenario with the strengthening of the background Walker circulation, the predictability of sea surface temperature in central Pacific has a significant response with a notable increase in summer and fall. Finally, the Gaussian approximation is shown to be accurate in computing the information gain, which facilitates the use of more sophisticated models to study the ENSO predictability.

physics.ao-ph↗
arXiv2022

An Efficient Routing Protocol for Quantum Key Distribution Networks

Quantum key distribution (QKD) can provide point-to-point information-theoretic secure key services for two connected users. In fact, the development of QKD networks needs more focus from the scientific community in order to broaden the service scale of QKD technology to deliver end-to-end secure key services. Of course, some recent efforts have been made to develop secure communication protocols based on QKD. However, due to the limited key generation capability of QKD devices, high quantum secure key utilization is the major concern for QKD networks. Since traditional routing techniques do not account for the state of quantum secure keys on links, applying them in QKD networks directly will result in underutilization of quantum secure keys. Therefore, an efficient routing protocol for QKD networks, especially for large-scale QKD networks, is desperately needed. In this study, an efficient routing protocol based on optimized link-state routing, namely QOLSR, is proposed for QKD networks. QOLSR considerably improves quantum key utilization in QKD networks through link-state awareness and path optimization. Simulation results demonstrate the validity and efficiency of the proposed QOLSR routing protocol. Most importantly, with the growth of communication traffic, the benefit becomes even more apparent.

quant-ph↗
arXiv2022

A Simple Multiscale Intermediate Coupled Stochastic Model for El Niño Diversity and Complexity

El Niño-Southern Oscillation (ENSO) is the most prominent interannual climate variability in the tropics and exhibits diverse features in spatiotemporal patterns. In this paper, a simple multiscale intermediate coupled stochastic model is developed to capture the ENSO diversity and complexity. The model starts with a deterministic and linear coupled interannual atmosphere, ocean and sea surface temperature (SST) system. It can generate two distinct dominant linear solutions that represent the eastern Pacific (EP) and the central Pacific (CP) El Niños, respectively. In addition to adopting a stochastic model for characterizing the intraseasonal wind bursts, another simple stochastic process is developed to describe the decadal variation of the background Walker circulation. The latter links the two dominant modes in a simple nonlinear fashion and advances the modulation of the strength and occurrence frequency of the EP and the CP events. Finally, a cubic nonlinear damping is adopted to parameterize the relationship between subsurface temperature and thermocline depth. The model succeeds in reproducing the spatiotemporal dynamical evolution of different types of the ENSO events. It also accurately recovers the strongly non-Gaussian probability density function, the seasonal phase locking, the power spectrum and the temporal autocorrelation function of the SST anomalies in all the three Niño regions (3, 3.4 and 4) across the equatorial Pacific. Furthermore, both the composites of the SST anomalies for various ENSO events and the strength-location bivariate distribution of equatorial Pacific SST maxima for the El Niño events from the model simulation highly resemble those from the observations.

physics.ao-ph↗